Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds / / Raphaël S. Ponge

• Record Nr.: UNINA9910788852103321
• Autore: Ponge Raphael <1972->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2008]; ©2008
• ISBN: 1-4704-0512-1
• Descrizione fisica: 1 online resource (150 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 906
• Disciplina: 515/.7242
• Soggetti: Hypoelliptic operators; Spectral theory (Mathematics); Calculus; Differentiable manifolds
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (pages 131-134).
• Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""1.1. Heisenberg manifolds and their main differential operators""; ""1.2. Intrinsic approach to the Heisenberg calculus""; ""1.3. Holomorphic families of Î?[sub(H)]DO[sub(S)]""; ""1.4. Heat equation and complex powers of hypoelliptic operators""; ""1.5. Spectral asymptotics for hypoelliptic operators""; ""1.6. Weyl asymptotics and CR geometry""; ""1.7. Weyl asymptotics and contact geometry""; ""1.8. Organization of the memoir""; ""Chapter 2. Heisenberg manifolds and their main differential operators""; ""2.1. Heisenberg manifolds""; ""2.2. Main differential operators on Heisenberg manifolds""""Chapter 3. Intrinsic Approach to the Heisenberg Calculus""; ""3.1. Heisenberg calculus""; ""3.2. Principal symbol and model operators.""; ""3.3. Hypoellipticity and Rockland condition""; ""3.4. Invertibility criteria for sublaplacians""; ""3.5. Invert ibility criteria for the main differential operators""; ""Chapter 4. Holomorphic families of Î?[sub(H)]DO[sub(S)]""; ""4.1. Almost homogeneous approach to the Heisenberg calculus""; ""4.2. Holomorphic families of Î?[sub(H)]DO[sub(S)]""; ""4.3. Composition of holomorphic families of Î?[sub(H)]DO[sub(S)]""""4.4. Kernel characterization of holomorphic families of Î?]DO[sub(S)]""; ; ""4.5. Holomorphic families of Î?]DO[sub(S)] on a general Heisenberg manifold""; ""4.6. Transposes and adjoints of holomorphic families of Î?[sub(H)]DO[sub(S)]""; ""Chapter 5. Heat Equation and Complex Powers of Hypoelliptic Operators""; ""5.1. Pseudodifferential representation of the heat kernel""; ""5.2. Heat equation and sublaplacians""; ""5.3. Complex powers of hypoelliptic differential operators""; ""5.4. Rockland condition and the heat equation""; ""5.5. Weighted Sobolev Spaces""""Chapter 6. Spectral Asymptotics for Hypoelliptic Operators""; ""6.1. Spectral asymptotics for hypoelliptic operators""; ""6.2. Weyl asymptotics and CR geometry""; ""6.3. Weyl asymptotics and contact geometry""; ""Appendix A. Proof of Proposition 3.1.18""; ""Appendix B. Proof of Proposition 3.1.21""; ""Appendix. Bibliography""; ""References""